MCVB treatment

It is instmctive to examine the symmetry of the standard tableaux function of highest EGSO population given in Table 10.2. The effects of the two symmetry 

It is important to reeognize why Eq. (10.7) is true. From Chapter 5 we have 

10 Four simple three-electron systems Table 10.3. Results of smaller VB calculations. 

Our ability to represent the wave flinetion for allyl as one standard tableaux function should not be considered too important. If we had ordered our 2/7 orbitals differently with respect to particle labels, there are cases where the A2 function would require using both standard tableaux functions. 

This happens when we consider the most important configuration using HLSP functions. The two Rumer diagrams are shown with dots to indicate the extra electron. 

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The HeJ ion has the archetype three-electron bond originally described by Pauling [1], and this section gives a description of MCVB calculation and SCVB treatments for this system. All of these use a Huzinaga 6-G Is function split (411), a 4-G 2s function and a pz function with the scale set to 0.9605. We take up the MCVB treatment first. 

The structure of CH2 was discussed by a completely MCVB treatment in Chapter 15. Here we look at it from an ROHF point of view. The structure of CH2 was uncertain for a number of years, but it is now known that the ground state is triplet with a bent geometry in C2V symmetry. Conventions dictate that CH2 be oriented with the C2-and z-axes coincident and the molecule in the y-z plane. Consequently the ground state is 5i, and the MO configuration is... 

Our treatments of ethylene are all carried out with two methylene fragments that have the a la b parts of both of their configurations doubly occupied in all VB stmctures used. The 12 electrons involved can be placed in the core as described in Chapter 9, which means that there are only four electrons, those for the C—C a and 7t bonds, that are in the MCVB treatment. For simplicity we shall rename the other two methylene orbitals a, and tti, where / = 1,2 for the two ends of the molecule. The Weyl dimension formula tells us that there are 20 linearly independent tableaux from four electrons distributed in four orbitals. When we use D2h s mimetry, however, only 12 of them are involved in eight Ai functions. 

This is, of course, the approach used by all of the early VB workers. In more recent times, after computing machinery allowed ab initio treatments, this is the sort of wave function proposed by Balint-Kurti and Karplus[34], which they called a multi structure approach. The present author and his students have proposed the multiconfiguration valence bond (MCVB) approach, which differs from the Balint-Kurti-Karplus wave function principally in the way the , are chosen. 

In this chapter we describe four rather different three-electron systems the it system ofthe allyl radical, the HeJ ionic molecule, the valence orbitals ofthe BeHmolecule, and the Li atom. In line with the intent of Chapter 4, these treatments are included to introduce the reader to systems that are more complicated than those of Chapters 2 and 3, but simple enough to give detailed illustrations of the methods of Chapter 5. In each case we will examine MCVB results as an example of localized orbital treatments and SCVB results as an example of delocalized treatments. Of course, for Li this distinction is obscured because there is only a single nucleus, but there are, nevertheless, noteworthy points to be made for that system. The reader should refer back to Chapter 4 for a specific discussion of the three-electron spin problem, but we will nevertheless use the general notation developed in Chapter 5 to describe the results because it is more efficient. 

In this section we give the results of MCVB and SCVB treatments of BeH using a conventional 6-3IG basis. Although there are some similarities to the HeJ ion, the lack of g-u symmetry in this case introduces a number of interesting... 

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